Under those circumstances you are fine. Your bags will be checked through to the states. All you will need to do is wing your way through Heathrow. A bit of a warning - you are in the midst of a larege transitional period for Heathrow Airport. There may and will be sudden changes to terminals as they move to close terminal two, expand terminal 3, and use terminal 5 for more of BA's flights. A number of the translatlantic flights, even with BA depart from terminal 3. At present, the shuttle flights come into Terminal 1. The transfer between the terminals is actually quite easy, using the underground moving walkways.
Have a great journey!
Fr Bill